Hessenberg matrix

Summary

An upper Hessenberg matrix is a square matrix whose entries below the first subdiagonal are zero; a lower Hessenberg matrix is its transpose. It is almost triangular, with one extra diagonal. Every complex square matrix is unitarily similar to an upper Hessenberg matrix, and this reduction takes finitely many steps. For this reason the QR algorithm for eigenvalues first brings a matrix to Hessenberg form.